Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On Euclidean Embeddings and Bandwidth Minimization
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Divide-and-conquer approximation algorithms via spreading metrics
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Geometry of Cuts and Metrics
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Integrality ratio for group Steiner trees and directed steiner trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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We introduce flow metrics as a relaxation of path metrics (i.e. linear orderings). They are defined by polynomial-sized linear programs and have interesting properties including spreading. We use them to obtain relaxations for several NP-hard linear ordering problems such as the minimum linear arrangement and minimum pathwidth. Our approach has the advantage of achieving the best-known approximation guarantees for these problems using the same relaxation and essentially the same rounding for all the problems and varying only the objective function from problem to problem. This is in contrast to the current state of the literature where each problem warrants either a new relaxation or a new rounding or both. We also characterize a natural projection of the relaxation.